Yse a DAX measure to calculate the sum of the duration for any events that fall on a given date. You can do this using a disconnected date table.
For example, if you have a disconnected date table called Date, and your event table is called Event, you can have a measure such as:
Filtered Duration =
MAX ( MIN ( 'Date'[Date] ), Event[StartDateTime] ),
MIN ( MAX ( 'Date'[Date] ), Event[EndDateTime] ),
'Event'[StartDateTime] <= MAX ( 'Date'[Date] )
&& 'Event'[EndDateTime] >= MIN ( 'Date'[Date] )